CONSTRUCTIONS OF SEGAL ALGEBRAS IN L1(G) OF LCA GROUPS G IN WHICH A GENERALIZED POISSON SUMMATION FORMULA HOLDS

Let G be a non-discrete locally compact abelian group, and mu be a transformable and translation bounded Radon measure on G. In this paper, we construct a Segal algebra S-mu(G) in L-1(G) such that the generalized Poisson summation formula for mu holds for all f is an element of S-mu(G), for all x is an element of G. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.